I would like to know which formula to use in order to optimize a portfolio based on highest Treynor and Jensens Alpha. I am aware that usually one optimize a portfolio by highest Sharpe ratio (the tangency portfolio) by following formula:

This is also what I've concluded. But is there no way to incorporate a reward for diversification? If not, how come mathematically, that it is not possible?
–
Jens JensenMay 20 '14 at 12:48

If you make your metric Sharpe-like, by including a measure of distributional width in the denominator, then there is of course a reward. If that measure is standard deviation, then the mathematics even works out to be nearly identical to Markowitz.
–
Brian BMay 20 '14 at 13:20

I do not really understand how to solve this. Is it possible to edit your answer with a more detailed description of how to solve the question?
–
Jens JensenMay 20 '14 at 22:09